In what situations ELUs should be used instead of RELUs?
ELU does not suffer from from dying neurons issue, unlike ReLU. While ELU can help you to acheive a better accuracy, it is a slower than ReLU because of its non linearity in its negative range.
Choosing a right activation function totally depends on situations but you need to also consider other similar types of activation function such as leaky ReLU.
Check this link out. It could be useful.